Most common node set up for textures
Let's break that down.


  Was wondering if there was a common, base style set up of nodes for
  use in cycles as a good basic starting point to just experiment with
  from with respect to textures and materials.


Yes, there is. Typically your surfaces are some sort of mix between a glossy reflection and a diffuse. Therefore most materials have


A mix node
A diffuse
A glossy


Some materials (basically metals) conduct electricity. They have the property of having a more mirror-like reflection towards the edges and more diffuse reflections towards the center. To model this effect in Cycles one typically used a layer weight or fresnel node feeding into the mix factor.

To find out more about this real world mimicking type of material, have a look at these tutorials by Andrew Price.


  Also, why would one want to use nodes in blender internal to do
  textures and materials? Couldn't you just do the same thing using the
  modifiers panel and properties panel?


Whatever material related work you do through the modifiers and properties panels escapes me. However, the use of nodes in the internal renderer engine allows for some extra effects like mixing two existing materials of different types (think halo and write for example). Related: Mix two materials in the Blender Internal Materials Nodes. Overall it's use cases are indeed quite rare for the average user.,